We know that emails aren't a written condition, but IMO this isn't the point.
It's whether such a condition does apply by virtue of custom and practice. There are no doubt reams of text books on contract law which include C&P. In short, just because it's not written does not mean it's not an enforceable term.
Thanks for this, do you know if their argument would hold up at a tribunal? Still unsure whether I should risk taking this all the way.
You haven't even taken the first step yet, so considerations of 'all the way' are premature IMO.
IMO, it is NOT a frivolous point and therefore may be advanced as regards PCN1. You would then get a reply. This might contain procedural improprieties which themselves are grounds for appeal irrespective of the initial defence.
But none of this is going to happen unless you make reps!